585 


EXCHANGE 


The  Measurement  of  Dielectric 
Constants 


DISSERTATION 


SUBMITTED  TO  THE  BOARD  OF  UNIVERSITY  STUDIES  OF 

THE  JOHNS  HOPKINS  UNIVERSITY  IN  CONFORMITY 

WITH  THE  REQUIREMENTS  FOR  THE  DEGREE 

OF  DOCTOR  OF  PHILOSOPHY 


BY 
JOHN  FITCH  KING 

February,  1921 


EASTON,  PA.: 
ESCHBNBACH  PRINTING  Co. 

1922 


The  Measurement  of  Dielectric 
Constants 


DISSERTATION 


SUBMITTED  TO  THE  BOARD  OF  UNIVERSITY  STUDIES  OF 

THE  JOHNS  HOPKINS  UNIVERSITY  IN  CONFORMITY 

WITH  THE  REQUIREMENTS  FOR  THE  DEGREE 

OF  DOCTOR  OF  PHILOSOPHY 


BY 

JOHN  FITCH  KING 
February,  1921 


EASTON,  PA.: 
ESCHENBACH  PRINTING  Co. 

1922 


ACKNOWLEDGMENT. 

The  writer  wishes  to  express  his  gratitude  to  Dr.  Walter  A.  Patrick 
under  whose  guidance  this  work  was  done  and  to  thank  Drs.  Frazer, 
Reid,  Lovelace  and  Thornton  for  laboratory  and  class  room  instruction. 
An  expression  of  appreciation  is  due  the  late  Professor  Granville  R.  Jone- 
for  his  interest  and  help. 

The  writer  also  takes  this  opportunity  to  thank  Dr.  E.  O.  Hulbert  and 
Mr.  Gregory  Breit  of  the  Department  of  Physics  who  were  frequently 
consulted  during  the  difficult  construction  of  the  dielectric  apparatus. 


THE  MEASUREMENT  OF  DIELECTRIC  CONSTANTS. 

This  preliminary  paper  contains  a  description  of  a  bridge  method  for 
measuring  dielectric  constants  of  liquids  in  which  use  is  made  of  audion 
bulbs  both  as  a  source  of  exciting  current  and  as  a  means  of  determining 
the  balance  point  of  the  bridge.  Our  interest  in  the  dielectric  constant 
is  due  to  the  suspected  close  relationship  that  exists  between  this  constant 
and  the  solvent  power  of  liquids.  That  there  is  a  relation  between  the 
swelling  powers  of  liquids  and  their  dielectric  constants  is  apparent  from 
a  casual  review  of  the  experimental  data.  However,  there  are  many 
exceptions  to  the  rule  and  our  effort  is  directed  toward  the  possibility  of 
finding  a  more  general  relationship. 

Accordingly,  we  planned  first  to  measure  the  dielectric  constants  of 
a  series  of  liquids  and  mixtures  of  the  same  and  also  the  swelling  power, 
or  as  it  is  incorrectly  called  the  "solvent"  power,  that  these  exerted  upon 
a  certain  sample  of  cellulose  nitrate. 

Our  choice  of  a  suitable  method  for  the  measurement  of  dielectric  con- 
stant was  greatly  influenced  by  the  result  of  a  year's  work  in  this  field  by 
one  of  the  authors.  This  work  (unpublished)  was  done  in  University 
College,  London,  together  with  Professor  F.  G.  Donnan  and  resulted  in 
the  conviction  that  there  is  no  satisfactory  method  for  the  measurement  of 
dielectric  constant  of  liquids  possessing  a  specific  conductivity  greater 
than  that  of  conductivity  water.  In  this  work  the  Drude1  method  as 
well  as  Schmidt's2  modification  was  carefully  investigated,  using  a  well 
constructed  apparatus  in  which  special  attention  was  paid  to  the  exciting 
energy  and  the  end-point  detectors.  A  30cm.  spark  induction  coil 
was  employed,  operated  with  a  mercury  break  interrupter.  This  induction 
coil  was  connected  to  a  Tesla  converter,  the  energy  from  which  was  used 
to  excite  the  primary  circuit  of  the  testing  apparatus.  Neon  tubes  were 
prepared  and  the  most  sensitive  ones  were  used  in  determining  the  end- 
point.  The  results  of  the  experiments  with  this  apparatus  showed  that 
neither  from  the  standpoint  of  precision  nor  from  the  standpoint  of  the 
ability  to  measure  the  dielectric  constants  of  conducting  liquids,  does 
this  apparatus  have  the  advantages  which  have  been  claimed  for  it  over 
other  methods.  When  liquids  that  possessed  a  conductivity  only  slightly 
greater  than  that  of  conductivity  water  were  used,  the  minima  became 


1  Drude,  Z  physik.  Chem.,  23,  267  (1897). 

2  Schmidt,  ibid.,  27, 343  (1898). 


very  obscure,  and  furthermore  during  the  measurement  a  large  increase 
in  the  temperature  of  the  liquid  was  observed,  indicating  that  energy 
absorption  was  taking  place.  This  energy  absorption  increased  with 
the  increase  in  frequency  of  the  electric  wave.  This  is  important  from 
the  chemist's  viewpoint  since  it  is  commonly  understood  that  an  increase 
in  the  frequency  of  the  electric  wave  enables  one  to  measure  the  dielectric 
constant  of  a  conducting  liquid. 

Many  experiments  were  made  with  the  well-known  bridge  method  as 
developed  by  Nernst.3  Special  attention  was  given  here  to  the  source 
of  alternating  current.  Electrically  driven  tuning  forks  of  various  fre- 
quencies within  the  telephonic  range  were  used,  as  well  as  a  variety  of 
other  well-known  interrupters.  The  sharpest  minima,  however,  were 
obtained  with  a  small  Wehnelt  break.  All  manner  of  changes  in  the 
apparatus  did  not  develop  an  arrangement  which  was  especially  satis- 
factory. The  principal  objection  was  the  lack  of  precision.  The  sources 
of  current  producing  the  more  symmetrical  electric  waves  gave  minima 
which  extended  over  a  large  portion  of  the  setting  scale. 

From  a  theoretical  consideration  of  the  distribution  of  an  alternating 
current  in  a  Wheatstone  bridge,  we  decided  to  use  as  our  source  of  alter- 
nating current  an  apparatus  which  would  furnish  a  symmetrical  wave. 
This  is  an  important  factor  in  the  measurement  of  dielectric  constant  for 
the  assurance  of  a  sharp  and  true  minim^t.  Professor  Flemming4  has  given 
it  consideration  in  his  statement,  "It  may  be  pointed  out  incidentally 
that  no  accurate  balance  or  well  defined  zero  can  be  obtained  unless  the 
electromotive  force  applied  to  the  bridge  has  a  very  true  sine  wave  form. 
Hence  no  arrangement  such  as  a  buzzer,  hummer  or  current  interrupter 
of  any  kind  can  be  substituted  for  the  sine  curve  alternator  or  for  an  al- 
ternator and  a  wave  filter." 

We  used  a  frequency  of  about  1000  cycles  per  second  since  this  is  within 
the  telephonic  range  and  gives  a  pitch  easy  to  detect  and  since  there  is 
nothing  to  be  gained  by  using  a  higher  frequency.  The  work  of  one  of 
us  cited  above  showed  that  there  is  greater  energy  absorption  at  higher 
frequencies.  Flemming  has  treated  this  matter  theoretically  and  has 
shown  that  greater  dissipation  of  current  due  to  the  dielectric  occurs  at 
higher  frequencies.  With  a  slightly  conducting  liquid  in  our  cell  we  have 
to  measure  the  capacity  similar  to  that  of  a  leaky  condenser.  Flemming 
has  shown  that  the  energy  loss  in  a  poor  dielectric  due  to  an  alternating 
current  can  be  divided  into  two  parts,  the  first  due  to  conductivity 
which  is  probably  electrolytic  in  nature  and  the  second  to  a  conductivity 
which  is  nearly  proportional  to  the  frequency.  The  first  is  the  regular 
direct  current  conductance  while  the  second  has  been  called  an  alternating 
current  conductance. 

1  Nernst,  Z.  physik.  Chem.,  14,622  (1894). 

4  Fleming,  Proc.  Phys.  Soc.  London,  [2]  23,  117  (1911). 


In  the  method  worked  out  by  Nernst,  the  ratio  arms  of  the  bridge 
consisted  of  two  resistances  and  the  other  arms  consisted  of  an  unknown 
capacity  which  was  balanced  by  a  measuring  condenser.  In  order  to 
make  the  impedance  in  the  ratio  arms  of  the  same  magnitude  as  the  im- 
pedance in  the  balancing  arms,  it  was  necessary  to  use  very  large  resist- 
ances with  the  possibility  of  introducing  self-induction  into  those  arms  of 
the  bridge.  We  used  air  condensers  in  all  four  arms.  Air  condensers 
are  to  be  desired  because  of  their  more  constant  capacity  and  the  smaller 
f  chance  for  leakage. 

Since,  with  a  conducting  solution  in  our  dielectric  cell  condenser,  we 
f  had  to  balance  a  leaky  condenser,  we  used  a  non-inductive  resistance 
:  shunted  around  the  measuring  condenser  in  the  balancing  arm  of  the  bridge. 
Although    Flemming4   has    shown  that  it  is  not   possible  to    duplicate 
a  leaky  condenser  by  means  of  a  condenser  and  a  resistance  in  parallel, 
we  were  able  to  prove  that  up  to  a  certain  limiting  value  of  shunted  con- 
ductivity it  was  possible  to  obtain  true  values  of  the  capacity  of  the  con- 
denser. 

Much  attention  has  been  given  by  conductivity  workers  and  workers 
on  the  bridge  method  for  the  measurement  of  dielectrics  to  the  phone  used 
to  detect  the  minima.  The  minimum  current  possible  in  the  bridge  is 
determined  by  the  current  necessary  to  excite  the  phones.  This  minimum 
current  is  still  large  enough  to  cause  trouble  in  the  matter  of  heating 
effects,  polarization,  etc.  A  small  current  is  to  be  desired,  but  using  a 
small  current  and  one  of  symmetrical  wave  form  much  difficulty  is  ex- 
perienced in  reaching  a  minimum.  To  overcome  this  difficulty  we  used 
the  thermo-ionic  amplifier  of  recent  development.  With  this  improved 
apparatus,  consisting  of  a  source  of  alternating  current  of  symmetrical 
wave  form,  a  symmetrical  bridge,  each  arm  of  which  offered  an  impedence 
of  the  same  magnitude,  and  with  an  extremely  small  current  flowing 
through  the  bridge,  the  use  of  which  was  made  possible  by  the  amplifier  in 
connection  with  the  telephones,  we  hoped  for  an  improvement  in  the  accur- 
acy of  our  measurements. 

The  Vreeland  oscillator  is  without  doubt  the  best  source  of  alternating 
current  of  sine  wave  form,  but  the  cost  of  the  Vreeland  oscillator  led  us 
to  turn  to  the  electron  tube  as  our  source  of  current.  By  an  arrangement 
in  which  an  electron  tube,  a  condenser  and  an  induction  coil  are  connected 
in  a  circuit,  it  is  possible  to  obtain  an  alternating  current  of  symmetrical 
wave  form.  With  this  arrangement  by  properly  varying  the  plate  voltage, 
the  temperature  of  the  filament,  the  capacity  and  the  induction,  it  is  possi- 
ble to  obtain  different  currents  varying  from  a  few  tenths  of  a  milliampere 
or  less  to  25  amperes  and  with  a  frequency  varying  from  ^  cycle  per 
second  to  50  million  cycles  per  second.6 

6  Hall  and  Adams,  /.  Am.  Chem.  Soc.,  41,  1515  (1919). 


PHONES 


BRIDGE 
ANPLIFHEIR 

DIELECTRIC   CONSTANT  APPARATUS 

We  used  the  "Marconi  Vacuum  Tube"  type  V.T.I.  In  the  drawing,  T  is  the  vac- 
uum tube,  C  the  condenser,  and  I  the  induction  coils.  The  audion  plate  was  charged 
with  120  volts  by  dry  cells  while  the  filament  was  heated  with  a  current  of  0 . 7  ampere 
and  4  volts  supplied  from  lead  storage  cells.  The  two  induction  coils  consisted  of 
about  300  turns  of  No.  32  wire  each  wound  around  a  laminated  iron  core.  The  lead 
to  the  bridge  was  coupled  to  this  with  about  50  turns  on  the  secondary  coil.  At 
C  are  two  variable  Murdock  condensers  connected  in  parallel.  By  adjustment  of  these 
condensers  we  obtained  a  frequency  of  about  1000  cycles  per  second.  During  the  first 
part  of  our  work  we  used  the  laboratory  current  to  charge  the  plates  in  the  electron 
tubes  both  in  the  amplifier  and  in  the  oscillator.  Great  difficulty  was  experienced 
from  external  noises  caused  from  other  electrical  apparatus  running  in  the  building 
which  tended  to  obscure  the  minimum  and  greatly  tried  the  patience  of  the  operator; 
but  when  dry  cells  were  used  to  supplant  the  laboratory  current  the  results  were  most 
gratifying. 

In  the  construction  of  the  bridge,  two  variable  Murdock  air  condensers  were  used  in 
the  ratio  arms.6  The  condensers  had  a  capacity  of  about  0 . 0005  microfarad  and  the 
scales  were  divided  into  180  divisions.  In  any  series  of  measurements  these  condensers 
were  set  and  the  moving  pointer  sealed  by  means  of  sealing  wax.  These  condensers 

6  These  condensers  as  well  as  most  of  the  wireless  apparatus  were  purchased  from 
the  Wireless  Specialty  Co.  of  Boston. 


9 

are  represented  by  d  and  C»  in  the  drawing.     In  the  measuring  arm  of  the  bridge  were 
the  following  parts. 

1.  A  variable  vernier  condenser,  C3  in  the  drawing,  "DeForest"  type,  with  a  ca- 
pacity of  0.0015  microfarad.     The  ccale  was  divided  into  100  divisions.     The  vernier 
had  a  capacity  of  about  180  degrees  per  scale  division.     The  pointer  on  this  scale  was  ex- 
tended about  75  cm.  to  an  enlarged  scale  of  some  2200  divisions  of  1  mm.  each,  thus  en- 
abling us  to  set  the  condenser  with  a  much  greater  precision.   In  making  a  measurement, 
the  setting  was  made  on  the  large  scale  and  then  the  accuracy  of  the  scale  was  tested 
by  means  of  the  vernier  condenser.      The  vernier  was  moved  by  means  of  a  lever 
operated  from  the  center  of  the  room.     This  was  done  to  prevent  the  introduction  of 
capacity  into  the  bridge  from  the  operator's  body.    If  after  making  a  setting  on  the  large 
scale,  the  vernier,  by  a  small  movement  to  the  right  and  to  the  left,  passed  through 
a  minimum,  we  assumed  the  setting  to  be  correct. 

2.  Connected  in  parallel  with  this  measuring  condenser  was  a  second  Murdock 
condenser,  C3',  from  which  about  half  of  the  plates  had  been  removed.     The  recording 
pointer  of  this  condenser  was  also  extended  to  an  enlarged  scale.     It  was  possible  to 
use  the  large  condenser  for  changes  in  dielectric  from  2  to  about  26  and  over  and  the 
small  condenser  for  changes  from  2  to  7,  gaining  a  5-fold  increase  in  sensitivity.     The 
vernier  setting-lever  was  used  for  testing  the  setting  of  the  minimum  when  either  con- 
denser was  used.    When  C3  was  used,  C3'  was  locked  in  a  fixed  position,  the  scale  of 
C3  calibrated  and  the  measurements  made.     When  it  was  desired  to  use  C3'  as  the 
measuring  condenser,  C3  was  locked  and  the  small  condenser  scale  was  calibrated. 

3.  RI  is  a  non-inductive  resistance  made  by  filling  a  conical  glass  tube  with  "Man- 
gani"  solution  (121    g.  of  mannitol  plus  41  g.  of  boric  acid).     The  resistance  of  this 
tube  could  be  varied  by  varying  the  distance  between  the  electrodes  or  by  moving 
a  plunger  down  into  the  ground  glass  conical  part  of  the  tube,  thereby  decreasing  the 
cross  section.     The  stem  of  the  plunger  fitted  into  a  hard  rubber  cap  which  was  threaded. 
The  small  thread  on  the  screw  of  the  cap  made  possible  a  very  sharp  setting  of  the  re- 
sistance.    This  was  extremely  important  when  any  great  conductivity  was  possessed 
by  the  liquid  being  measured.     In  some  cases  it  was  found  that  turning  the  cap  one 
or  two  mm.,  involving  the  very  slight  accompanying  displacement  of  the  plunger  in 
the  tube,  entirely  obscured  the  minimum.     Previous  workers  have  called  attention  to 
the  importance  of  the  resistance  used  to  compensate  the  conductivity.     It  has  been 
suggested  that  as  the  conductivity  increased  and  the  electrodes  in  the  liquid  resistance 
were  moved  closer  together,  a  capacity  was  introduced  in  the  resistance  tube  which  in- 
volved an  error  in  the  capacity  of  the  measuring  condenser.     That  this  is  not  the  true 
explanation  can  easily  be  shown  by  a  consideration  of  the  voltage  consumption  in  the 
measuring  arm  of  the  bridge.     A  simple  calculation  is  sufficient  to  illustrate  this  point. 

Consider  the  bridge,  with  capacities  C\  and  C2  balanced  against  capacities  C3  and 
C4  the  latter  being  shunted  with  resistances  R\  and  R2  respectively.  Then  Zi/Z2  =  Z3/Z4 
where  Z  is  the  impedance;  if  C\  =  Cz,  and  both  C\  and  €2  are  air  condensers,  Zi  =Zz,  and 
therefore  Z3  =  Z4. 

Let  us  suppose  that  Ct  is  composed  of  2  concentric  cylinders  0.2  cm.  apart  and 
having  an  electrode  surface  of  50  sq.  cm.  Furthermore,  let  the  dielectric  be  alcohol 
having  a  dielectric  constant  of  25  and  a  specific  conductivity  of  1  X  10  ~7  mho. 

The  capacity  of  such  a  condenser  is  Ka/4wd  900,000  =  0.00055  mf.  The  re- 
sistance of  such  a  cell  is  therefore  (50/0.2)  X  10 ~7  =  2.5  X  10 ~6 mho  =  0.4  X  105ohm. 

The  impedance  of  the  above  capacity  and  resistance  in  parallel  may  be  most  easily 
calculated  by  obtaining  the  vectorial  sum  of  the  admittances  due  to  capacity  and  re- 
sistance. The  admittance  due  to  capacity  at  a  frequency  of  1000  is  2ir.  1000C  =  2  X 
3. 1416  X  1000  X  5  X  10-^  =  3. 1  X  10 ~6.  Therefore  the  admittance  of  the  combina- 


10 


tion  is  V(2.5  X  lO"6)2  +  (3.1  X  lO"6)2  =  2.52  X  lO"6.    The  impedance  is  1/2.52 
X  10"6  =  0.396  X  K^ohm. 

This  calculation  shows  that  the  impedance  of  the  whole  bridge  arm  is  largely 
determined  by  that  of  the  resistance  alone  and  that  the  quantity  which  we  wish  to 
measure,  the  capacity,  only  slightly  affects  the  total  impedance.  In  other  words,  an 
accurate  measurement  of  capacity  cannot  be  made  at  a  frequency  of  1000  cycles  per 
second  if  the  impedance  due  to  resistance  is  less  than  that  due  to  capacity.  This  is 
an  important  consideration  for  the  determination  of  the  limit  of  conductivity.  It  has 
been  commonly  overlooked  in  dielectric-constant  measurements  of  conducting  solutions. 

4.  In  the  fourth  arm  of  the  bridge  was  a  condenser,  C4,  shunted  by  a  Mangani 
solution  resistance.  This  condenser  acted  as  a  tare  condenser  and  the  resistance  was 
used  to  balance  the  conductivity  of  the  liquid  when  the  dielectric  cell  condenser  was 
placed  on  the  Cs  arm  of  the  bridge  in  the  differential  method  of  measurement  which  was 
used.  Our  purpose  in  finally  adopting  the  differential  method  was  to  eliminate  any 
errors  due  to  an  unsymmetrical  arrangement  of  the  bridge  such  as  different  self-in- 
ductances of  the  wires,  mutual  capacities  of  the  condensers,  etc.  Also  by  the  differential 
method  twice  the  ordinary  displacement  on  the  measuring  scale  is  obtained  for  a  given 
change  in  dielectric. 

The  dielectric  cell  was  composed  of  two  co-axial  platinum  cylinders,  2.2  cm.  X 
6 . 3  cm.  and  1 . 9  cm.  X  6 . 3  cm.,  respectively,  which  were  set  in  the  ground  glass  stopper 
of  a  glass  cup.  This  cup  was  mounted  on  a  hard  rubber  base.  The  platinum  cylinders 
were  firmly  fastened  at  each  end  to  prevent  any  possible  displacement  during  a  set  of 
measurements.  These  cylinders  as  well  as  the  cup  were  easily  cleaned  between  measure- 
ments by  washing  several  times  with  alcohol  and  ether  and  then  drying  in  a  stream  of 
air.  It  was  so  arranged  that  the  whole  dielectric  cell  could  be  placed  in  a  holder  in 
a  thermostat  if  at  any  time  the  accuracy  of  the  work  should  demand  close  temperature 
control.  The  dielectric  cell  was  arranged  by  means  of  a  rocking  commutator  so  that 
it  could  be  placed  in  parallel  first  with  C4  and  a  reading  taken  and  then  in  parallel  with 
C8  and  the  difference  in  reading  taken.  During  the  calibration  of  the  scale  and  during 
any  series  of  measurements,  Ci,  C2,  and  C4  were  sealed,  Cs  being  the  only  condenser 
whose  capacity  was  changed. 

The  amplifier  was  a  two-step  type  triode  E  to  which  a  third  step  was  added  by  means 
of  an  amplifying  transformer  and  an  electron  tube,  thus  giving  a  1000  fold  amplification. 
The  plates  were  charged  at  40  volts  from  dry  cells  and  the  filaments  were  heated  by  a 
current  of  0 . 7  ampere  and  6  volts  from  lead  storage  cells.  This  amplifier  was  used  in 
connection  with  a  set  of  Baldwin  wireless  telephones.  These  telephones  have  non- 
adjustable  mica  diaphragms  and  were  especially  suited  for  wireless  work  for  the  recep- 
tion of  very  weak  signals.  Their  resistance  was  2000  ohms.  In  any  determination,  the 
amplifier  was  adjusted  by  changing  the  temperature  of  the  filaments  to  give  the  greatest 
sensitivity  and  then  was  not  changed  during  an  entire  calibration  and  set  of  measure- 
ments. This  was  in  keeping  with  the  care  always  exercised  during  a  set  of  readings  to 
vary  nothing  but  the  liquid  in  the  dielectric  cell  and  the  capacity  of  the  measuring  con- 
denser. It  was  only  by  employing  the  greatest  precaution  along  these  lines  that  con- 
sistent and  comparable  results  could  be  obtained.  For  instance,  before  the  rocking 
commutator  was  used  in  the  differential  method  of  measurement,  a  wire  was  moved 
from  C4  to  Ci  in  order  to  change  the  dielectric  cell  from  parallel  with  C4  to  parallel  with 
C|.  It  was  discovered  that  the  movements  of  this  fine  short  wire  caused  the  shifting  of 
the  minimum  many  divisions  on  the  recording  scale.  Again,  before  the  final  setting 
was  made  by  the  use  of  the  vernier  condenser  lever  operated  at  a  distance  from  the 
bridge,  it  was  found  that  effects  produced  by  the  operator's  body  either  entirely  ob- 
scured the  minimum  or  shifted  it  a  few  hundred  divisions. 


11 

The  first  set  of  measurements  on  the  bridge  was  made  for  the  purpose 
of  determining  the  sensitivity  of  the  apparatus.  Before  using  the  differ- 
ential method  it  was  found  that  we  were  able  to  get  very  sharp  minima 
when  the  ratio  of  the  condensers  in  the  ratio  arms  was  other  than  one 
to  one.  This  made  it  possible  to  magnify  the  deflection  of  the  dielectric 
cell  on  the  measuring  condenser.  With  benzene  in  C±,  the  dielectric 
cell,  C3  the  measuring  condenser  gave  in  4  experiments,  430,  430,  430, 
and  390;  with  ether  it  gave  840,  905,  1070,  and  1205,  respectively. 

In  the  last  measurement  a  change  in  dielectric  of  from  2.22  to  4.35 
caused  a  change  on  the  setting  scale  of  the  measuring  condenser  of  815 
divisions,  which  means  (setting  to  one  division  on  the  scale  and  one  di- 
vision is  one  millimeter)  that  one  division  on  the  scale  is  equivalent  to  a 
change  in  dielectric  of  0.0026.  These  measurements  could  be  made  on  Cs'. 
When  made  on  C$'  which  possessed  a  5-fold  sensitivity,  one  scale  division 
was  equivalent  to  a  change  in  dielectric  of  0.0005.  No  attempt  was  made 
to  carry  this  study  further  as  it  was  not  desired  to  reach  this  sensitivity. 
For  our  measurements  we  needed  a  sensitivity  which  would  keep  the  read- 
ings of  a  change  in  dielectric  of  from  2  to  26  on  the  scale. 

A  set  of  measurements  was  made  by  the  differential  method  and  the 
same  satisfactory  balancing  of  the  bridge  was  obtained. 

Investigation  was  next  made  of  the  effect  of  an  added  non-inductive 
resistance  to  an  air  condenser  whose  capacity  was  being  measured  by  the 
differential  method.  This  resistance  was  balanced  out  by  a  resistance 
in  parallel  to  the  condenser  in  the  balancing  arm. 

a.  b.  a-b.         diff. 

Condenser  alone 497        293        204 

Condenser  plus  resistance  in  parallel 505        260        245        41 

As  the  resistance  decreased,  the  difference  between  the  true  capacity 
and  the  observed  capacity  increased.  Next  a  22,000-ohm  resistance  was 
shunted  around  the  condenser  whose  capacity  was  being  measured.  As 
the  capacity  was  increased,  the  amount  that  the  minimum  was  shifted 
due  to  the  shunted  resistance  decreased.  It  was  also  found  that  there 
was  less  shifting  of  the  minimum  due  to  the  shunted  resistance  if  the  ratio 
condensers  as  1:1.  The  reason  for  this  can  be  seen  from  the  following 
calculation. 

If  the  impedance  of  the  ratio  arms  is  the  same,  i.  e.,  if  C\  =  C2,  then  C$ 
=  C±  in  the  presence  of  conductivity  due  to  ,R  only  on  condition  that  Cz 
is  shunted  with  an  equal  resistance.  On  the  other  hand,  if  C\  does  not 
equal  C2,  the  ratio  of  C3  to  C4  will  not  equal  the  ratio  of  C\  to  C2  even  under 
the  condition  that  R&  is  equal  to  R^.  A  single  calculation  is  sufficient  to 
bring  out  this  point. 

Let  C/C2  =  a/b;  thenZ3/Z4  =  b/a;  orA3/A4  =  a/b  (1) 

where  Z  is  the  impedance,  and  A  is  the  admittance.  Further  let  R3  =  R*  —  x.  A 
=  the  vectorial  sum  of  C3  + 


12 


=  VcJ  +  (!/*»);     and  ^  =  Vc42+(i/*2) 
FromEq.  loVc 


Squaring,  a'  C42  +       =  &2  C32  +  ? 


=  j   , 


a2      a2  (a2  • —  fr2) 
&~2+  62  a2  C42  x* 
C,      a  .       /a2  -62          i  (3) 


From  this  general  equation  one  can  see  that  the  ratio  of  Ct  to  C"4  is 
equal  to  the  ratio  of  C\  to  C2  only  when  the  product  C4  x  is  large.  Inas- 
much as  C  is  the  capacity  of  the  condenser  being  measured  we  can  increase 
the  product  only  by  working  with  dielectrics  of  small  conductivities,  that 
is  of  large  values  of  x.  In  other  words,  it  is  possible  to  obtain  a  greater 
sensitivity  by  making  the  ratio  of  the  ratio  condensers  greater  than  1; 
however,  this  cannot  be  done  for  liquids  having  appreciable  conductivity. 

The  effect  of  the  introduction  of  the  maximum  conductivity  of  the 
Mangani  resistance  tubes  shunted  around  an  air  condenser  was  studied. 
As  shown  by  the  following  observation,  no  appreciable  shifting  of  the  mini- 
mum resulted. 

c.  6.  a-b. 

Ai^  condenser  alone   1488  321  1167 

Air  condenser  plus  maximum  conductivity  of  re- 

sistancetube 1498  330  1168 

The  same  results  were  obtained  when  the  dielectric  cell  was  used. 

Dielectric  cell  alone, 

c.  6.  a- 6. 

Empty 1636  1588  48 

Filled  with  ether 1701  1523  178 

Dielectric  cell  plus  maximum  conductivity  of 
resistance  tube, 

Empty 1633  1585  48 

Filled  with  ether 1700  1522          178 

In  all  measurements  of  dielectric  constants  only  those  liquids  were  meas- 
ured whose  conductivity  could  be  balanced  out  with  the  tested  Mangani 
solution  resistances. 

The  condensers  in  the  ratio  arms  were  now  set  at  90,  i.  e.,  at  a  ratio  of 
1:1,  condensers  Ci,  Qj,  and  C4  were  sealed,  Ca  was  locked  into  position  and 
the  scale  on  Ca  was  calibrated  by  filling  the  dielectric  cell  with  the  above 
liquids.  The  calibration  curve  is  given  on  the  chart  with  the  curves  for  the 
dielectric  measurements. 


13 
CALIBRATION  DATA, 

Liquid.  D.  C.  a.  b.  a-b. 

Carbon  tetrachloride 2.25  1268  1160  108 

Ether 4.35  1320  1115  205 

CfiH6  +  CeHeNOa 15.9  1380  860  720 

Alcohol 25.8  1795  640  1155 

The  following  tables  give  the  results  of  the  dielectric  measurements 
of  the  different  mixtures  with  interpolation  values  from  the  curves.  The 
points  on  the  calibration  curve  were  re-checked  between  measurements 
so  as  to  assure  no  change  in  the  values  of  the  bridge.  The  liquids  were 
not  allowed  to  stand  exposed  to  the  air  during  a  measurement,  because  in 
some  cases  the  conductivity  increase  due  to  the  absorption  of  water  vapor 
from  the  air  was  such  as  to  introduce  an  error  in  the  observed  value  of  the 
capacity  of  the  dielectric  cell.  The  conductivity  of  alcohol  was  observed 
to  increase  considerably  upon  exposure  to  the  air  for  a  few  seconds.  At 
the  end  of  a  half  hour  or  less  the  conductivity  had  increased  beyond  that 
which  could  be  balanced  out  with  the  maximum  conductivity  of  the  Man- 
gani  resistances. 

DIELECTRIC  CONSTANTS  OF  MIXTURES  OF  BENZENE  IN  ETHYL  ALCOHOL. 

Dielectric 
constant. 

20.6 

23.2 
25.8 


DIELECTRIC  CONSTANTS  OF  MIXTURES  OF  ETHER  IN  ALCOHOL. 

Alcohol  %  Dielectric 

by  weight.  constant. 

80  20.6 

90  23.2 

100  25.8 


DIELECTRIC  CONSTANTS  OF  MIXTURES  OF  CARBON  TETRACHLORIDE  IN  ALCOHOL. 


Alcohol  % 
by  weight. 

Dielectric 
constant. 

Alcohol  % 
by  weight. 

Dielectric 
constant. 

Alcohol  % 
by  weight. 

0 

2.28 

40 

10.8 

80 

10 

4.3 

50 

13.1 

90 

20 

6.5 

60 

15.5 

100 

30 

8.6 

70 

18.0 

Alcohol  % 
by  weight. 

Dielectric 
constant. 

Alcohol  % 
by  weight. 

Dielectric 
constant. 

0 

4.35 

40 

10.9 

10 

5.7 

50 

13.1 

20 

7.2 

60 

15.5 

30 

8.9 

70 

18.0 

Alcohol  % 
by  weight. 

Dielectric 
constant. 

Alcohol  % 
by  weight. 

Dielectric 
constant. 

Alcohol  % 
by  weight. 

Dielectric 
constant. 

0 

2.25 

40 

14.5 

80 

22.6 

10 

5.4 

50 

17.0 

90 

24.2 

20 

8.6 

6' 

19.1 

100 

25.8 

30 

11.7 

70 

20.9 

Summary. 

1.  A  bridge  method  for  the  measurement  of  dielectric  constants  is 
described. 

2.  Preliminary  measurements  of  the  dielectric  constants  of  mixtures 
of  ethyl  alcohol  and  benzene,  ethyl  alcohol  and  ether,  and  ethyl  alcohol 
and  carbon  tetrachloride  are  given. 


BIOGRAPHY. 

John  Fitch  King  was  born  in  Ohio,  October  13,  1894.  His  early  educa- 
tion was  received  in  the  public  schools  of  Youngstown,  Ohio.  His  pre- 
paratory work  for  college  was  done  in  Rayen  School  in  Youngstown.  He 
attended  Oberlin  College  and  the  University  of  Wisconsin  and  received 
the  degree  of  Bachelor  of  Arts  from  Oberlin  College  in  1917.  In  the  fall 
of  1917  he  was  enrolled  as  a  student  in  the  graduate  department  of  chem- 
istry of  Johns  Hopkins  University.  February,  1918,  he  enlisted  in  the 
U.  S.  Army  and  was  stationed  at  the  University  laboratory  in  research 
on  war  gases.  The  following  school  year  was  spent  at  Harvard  University 
where  he  received  the  degree  of  Master  of  Arts.  In  the  year  1919-1920 
he  returned  to  the  Johns  Hopkins  University.  He  was  appointed  In- 
structor of  Chemistry  in  the  University  September,  1920. 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


AN  INITIAL  PINE  OF  25  CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


I935 

3nffl«^Q  /« 

OCT  31   1935 

vwjan  OJ/Q 

) 

C           ^3U**» 

JAM  0  0  1QCQ 

JM!X  ^  o  IJOJ 

r. 

S£j£    *Hfe 

•••• 

->.,  «:  V 

Mi 

JAN    2     TQ46 

... 

'.-n^f 

26FebDEAD 

LD  21-100m-7,'33 

Binder 
Gaylord  Bros. 

Makers 
Syracuse,  N.  Y. 

PAT.  JAN  21,  1903 


YC   1106 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 

'.       •* 


